Exposure method

ABSTRACT

An exposure method includes the steps of illuminating a mask that has a contact hole pattern using an illumination light, and projecting, via a projection optical system, the contact hole pattern onto a substrate to be exposed, wherein three lights among diffracted lights from the contact hole pattern interfere with each other, wherein said mask is an attenuated phase shift mask, and wherein said illumination light forms a radial polarization illumination.

BACKGROUND OF THE INVENTION

The present invention relates generally to exposure, and moreparticularly to an exposure method that is used to fabricate variousdevices, such as semiconductor chips, display devices, sensing devicesand image pick-up devices, and fine contact hole patterns used formicromechanics. Here, the micromechanics is technology for applying thesemiconductor IC fabrication technique for fabrications of a finestructure, thereby creating an enhanced mechanical system that mayoperate at a level of micron.

The photolithography technology for fabricating fine semiconductordevices has conventionally used a projection exposure apparatus thatuses a projection optical system to project and transfer a mask (orreticle) pattern onto a wafer. The mask pattern includes a contact. Asthe critical dimensions of the circuit layout become smaller, it hasbecome more difficult to resolve a fine contact hole stably. A transferof the pattern with high resolution requires a selection of optimalexposure conditions (such as kinds of masks, illumination condition,etc.) in accordance with kinds of patterns. Moreover, a stabilization ofan imaging performance requires a large depth of focus, and theillumination condition affects the depth of focus.

The contact hole pattern includes several kinds, such as a contact holesequence that periodically arranges contact holes that are adjacent eachother and an isolated contact hole that is isolated. A matrix patternform that arranges a square hole and a checker pattern form thatalternately arranges each sequence are known as the contact holesequence. An actual circuit pattern includes both of the matrix patternand checker pattern. The illumination condition for the circuit patternincluding only the matrix pattern or the circuit pattern including thematrix pattern and checker pattern is already proposed. For example, anannular illumination is suitable for the illumination condition for thecircuit pattern including the matrix pattern and checker pattern. Thecontact hole pattern that has a rectangle form is known. See, forexample, Hochul Kim et al., “Layser Specific Illumination Optimizationby Monte Carlo Method,” Optical Microlithography XVL, Anthony Yen,Editor, Proceedings of SPIE, Vol. 5040 (2003), pp. 244-250.

A binary mask, a phase shift mask, and an attenuated phase shift maskare known as a kind of mask. The illumination condition includes apolarization condition, a tangential polarization is suitable for a twobeam interference, and a radial polarization is suitable for a four beaminterference. A polarization control is important technology in theexposure apparatus that includes the projection optical system with highNA, such as an immersion exposure apparatus.

Japanese Patent Applications, Publication Nos. 2000-040656, 2003-203850,2004-272228 and 2003-318100 are proposed as other conventionaltechnology.

If 0^(th) diffracted light is set as a center of pupil in the projectionoptical system, checker pattern generates ±1^(th) diffracted light insix directions of around the center of pupil in the projection opticalsystem. Although the two beam interference is effective for theresolution of line, the resolution of contact hole needs three or morebeam. If three beam are suitably arranged in the pupil, k₁ of Rayleighequation reduces, the finer is promoted. Here, Rayleigh equation isexpressed by the following equation using a resolution R of theprojection exposure apparatus, a wavelength λ of a light source, anumerical aperture NA of the projection optical system, and a processconstant k₁ determined by a development process.R=k ₁ (λ/NA)  (1)

The checker pattern has a lot of the number of 1^(th) diffracted lightthat can enter the pupil, and three beam can be easily arranged in thepupil. Therefore, the contact hole pattern that includes only checkerpattern will push forward low k1. However, the analysis of optimalexposure conditions for checker pattern including optimal polarizationcondition for the three beam interference is not fully progressing.

BRIEF SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to an exposure methodthat improves a resolution performance of a checker pattern.

An exposure method of one aspect of the present invention includes thesteps of illuminating a mask that has a contact hole pattern using anillumination light, and projecting, via a projection optical system, thecontact hole pattern onto a substrate to be exposed, wherein saidcontact hole pattern is a checker pattern that includes a periodicpattern, in which plural contact holes are arranged in a first directionat a first pitch, and arranged in a second direction perpendicular tothe first direction at a second pitch, while shifting by half a pitch,wherein an effective light source formed on a pupil plane in theprojection optical system by the illumination light has six poles,wherein a distance between centers of gravity of the six poles and anoptical axis of the projection optical system is commonly α, whereinsaid centers of gravity of the six poles are located around the opticalaxis in a direction of an angle a to the first direction, wherein saidangle α is 0, 2α, π−2α, π, π+2α, and 2π−2α, wherein Pxo/2=(Px/2) NA/λ,Pyo/2=(Py/2) NA/λ, α=tan⁻¹ (Pxo/(2Pyo)), and α=1(4(Pyo/2)/sin (2a)) aresatisfied, where Px is the first pitch, Py is the second pitch, NA is anumerical aperture of the projection optical system, and λ is awavelength of the illumination light, and wherein three beam amongdiffracted lights from the contact hole pattern interfere with eachother.

An exposure method according to another aspect of the present inventionincludes the steps of illuminating a mask that has a contact holepattern using an illumination light, and projecting, via a projectionoptical system, the contact hole pattern onto a substrate to be exposed,wherein three beam among diffracted lights from the contact hole patterninterfere with each other, wherein said mask is an attenuated phaseshift mask, and wherein said illumination light forms a radialpolarization illumination.

An exposure method according to still another aspect of the presentinvention includes the steps of illuminating a mask that has a contacthole pattern using an illumination light, and projecting, via aprojection optical system, the contact hole pattern onto a substrate tobe exposed, wherein three beam among diffracted lights from the contacthole pattern interfere with each other, wherein said mask is a binarymask, and wherein said illumination light forms a tangentialpolarization illumination or unpolalized polarization illumination.

Other objects and further features of the present invention will becomereadily apparent from the following description of the preferredembodiments with reference to the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram of an exposure apparatus of oneembodiment according to the present invention.

FIG. 2A is a schematic plane view of one example of an aperture stopthat is applicable to the exposure apparatus shown in FIG. 1, and FIG.2B is a plane view of a basic example of a mask pattern in the exposureapparatus shown in FIG. 1.

FIG. 3A is a schematic plane view of a radial polarization of anillumination light, FIG. 3B is a view of a polarization state of threebeam on a pupil plane in a polarization state of two light sources shownin FIG. 3A, FIG. 3C is a schematic plane view of a tangentialpolarization of an illumination light, and FIG. 3D is a polarizationstate of three beam on a pupil plane in a polarization state of twolight sources shown in FIG. 3C.

FIG. 4A is a plane view of one example of a mask pattern shown in FIG. 1that applied the basic pattern shown in FIG. 2B, and FIG. 4B is a planeview of a diffracted light from the pattern shown in FIG. 4A.

FIG. 5 is a view for explaining a three beam interference by shiftingthe pupil shown.

FIGS. 6A and 6B are schematic plane views for explaining a three lightsinterference of a diffracted light on the pupil.

FIG. 7 is a graph of a relationship between a half pitch and a contrastthat depend on a polarization state in a first embodiment.

FIG. 8 is a graph of a relationship between a half pitch and a contractthat depend on a σ in a first embodiment.

FIG. 9 is a graph of a relationship between a half pitch and a depth offocus that depend on a σ in a first embodiment.

FIG. 10 is a graph of a relationship between a defocus and a contrastthat compared a small σ and annular illumination with a hexapoleillumination.

FIG. 11 is a graph of a relationship between a defocus and a CD thatcompared a small σ and annular illumination with a hexapoleillumination.

FIG. 12 is a graph of a relationship between a half pitch and a depth offocus that depend on a polarization state in a second embodiment.

FIG. 13 is a graph of a relationship between a half pitch and a depth offocus that depend on a σ in a second embodiment.

FIG. 14 is a graph of a relationship between a half pitch and a depth offocus that depend on a σ in a third embodiment.

FIG. 15 is a graph of a relationship between a half pitch and a depth offocus that depend on a σ in a third embodiment.

FIG. 16A is a schematic plane view of an aperture stop having a shapethat is not applied to the aperture stop of the exposure apparatus shownin FIG. 1, FIG. 16B is a schematic plane view of a two beam interferencewhen a direction of a light source does not accord with a direction of apattern, and FIG. 16C is a schematic plane view of a four lightsinterference when a direction of a light source does not accord with adirection of a pattern.

FIG. 17A is a schematic plane view of a phase shift mask that includes amatrix contact hole pattern, and FIG. 17B is a schematic plane view of aposition of a diffracted light in the pattern shown in FIG. 17A.

FIG. 18A is a schematic plane view of a circular effective light sourceshape, and FIG. 18B is a schematic plane view of an annular effectivelight source shape.

FIG. 19A is a graph of a relationship between a pitch and a contrastwhen the contact hole pattern shown in FIG. 17A is illuminated by theeffective light source shape shown in FIG. 18A, and FIG. 19B is a graphof a relationship between a pitch and a depth of focus when the contacthole pattern shown in FIG. 17A is illuminated by the effective lightsource shape shown in FIG. 18A.

FIG. 20 is a schematic plane view for explaining an insertion method ofan auxiliary pattern for an isolated pattern.

FIGS. 21A to 21D are schematic plane views for explaining an insertionmethod of an auxiliary pattern for an isolated pattern.

FIG. 22 is a schematic plane view of a mask pattern that inserted theauxiliary pattern in a fourth embodiment.

FIGS. 23A to 23E are schematic plane view for explaining a formingprocess of the mask pattern shown in FIG. 22.

FIG. 24 is a view of a resolution result of the mask pattern shown inFIG. 22.

FIG. 25 is a schematic plane view of a target pattern in a fifthembodiment.

FIG. 26 is a schematic plane view of a mask pattern that inserted anauxiliary pattern in the pattern shown in FIG. 25.

FIG. 27 is a schematic plane view of a mask pattern that insertedanother auxiliary pattern in the pattern shown in FIG. 25.

FIG. 28 is a view of a resolution result of the pattern shown in FIG.26.

FIG. 29 is a view of a resolution result of the pattern shown in FIG. 26by a different exposure condition.

FIG. 30A is a schematic plane view of a target pattern in a sixthembodiment, and FIG. 30B is a schematic plane view of a mask pattern ofchecker that inserted an auxiliary pattern in the pattern shown in FIG.30A.

FIG. 31 is a schematic plane view of an effective light source shape toexpose the mask pattern shown in FIG. 30B.

FIG. 32A is a view of an exposure result of the mask pattern shown inFIG. 30B at a best focus, and FIG. 32B is a view of an exposure resultof the mask pattern shown in FIG. 30B at a defocus.

FIG. 33A is a schematic plane view of another target pattern in a sixthembodiment, and FIG. 33B is a schematic plane view of a mask pattern ofchecker that inserted an auxiliary pattern in the pattern shown in FIG.33A.

FIG. 34 is a schematic plane view of an effective light source shape toexpose the mask pattern shown in FIG. 33B.

FIG. 35A is a view of an exposure result of the mask pattern shown inFIG. 33B at a best focus, and FIG. 35B is an exposure result of the maskpattern shown in FIG. 33B at a defocus.

FIG. 36A is a schematic plane view of further another target pattern ina sixth embodiment, and FIG. 36B is a schematic plane view of a maskpattern of checker that inserted an auxiliary pattern in the patternshown in FIG. 36A.

FIG. 37A is a view of an exposure result of the mask pattern shown inFIG. 36B at a best focus, and FIG. 37B is a view of an exposure resultof the mask pattern shown in FIG. 36B at a defocus.

FIG. 38 is a schematic plane view of further another target pattern in asixth embodiment.

FIG. 39 is a schematic plane view of an effective light source shape toexpose the mask pattern shown in FIG. 38.

FIG. 40A is a view of an exposure result of the mask pattern shown inFIG. 38 at a best focus, and FIG. 40B is a view of an exposure result ofthe mask pattern shown in FIG. 38 at a defocus.

FIGS. 41A and 41B are schematic plane views of a conventional effectivelight source shape.

FIG. 42A is a view of an exposure result of the mask pattern shown inFIG. 38 at a best focus, and FIG. 42B is a view of an exposure result ofthe mask pattern shown in FIG. 38 at a defocus.

FIG. 43 is a flowchart for explaining a method for fabricating devices(semiconductor chips such as ICs, LSIs, and the like, LCDs, CCDs, etc.).

FIG. 44 is a detail flowchart of a wafer process in Step 4 of FIG. 43.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Hereinafter, referring to FIG. 1, a description will be given of anexposure apparatus 100 of one aspect according to the present invention.Here, FIG. 1 is a schematic block diagram of the exposure apparatus 100.The exposure apparatus 100 includes, as shown in FIG. 1, an illuminationapparatus 110, a mask (reticle) 130, a projection optical system 140,and a main control unit 150.

The exposure apparatus 100 is an immersion exposure apparatus immerses aspace between a final surface (final lens) of the projection 140 at asubstrate 170 side and the substrate 170 in a liquid 180, and exposes apattern of the mask 130 onto a substrate 170 via the liquid 180.Although the exposure apparatus 100 of the instant embodiment is astep-and-scan manner projection exposure apparatus, the presentinvention is applicable to a step-and-repeat method and other exposuremethod.

The illumination apparatus 110 illuminates the mask 130 that has acircuit pattern to be transferred, and includes a light source sectionand an illumination optical system.

The light source section includes a laser 112 as a light source and abeam shaping system 114. The laser 112 may be pulsed laser such as anArF excimer laser with a wavelength of approximately 193 nm, a KrFexcimer laser with a wavelength of approximately 248 nm, an F₂ laserwith a wavelength of approximately 157 nm, etc. A kind of laser, thenumber of laser, and a type of light source section is not limited.Moreover, the light source applicable for the light source section isnot limited to the laser 112, and may use one or more lamps such as amercury lamp and a xenon lamp.

The beam shaping system 114 uses, for example, a beam expander, etc.,with a plurality of cylindrical lenses. The beam shaping system 114 cancovert an aspect ratio of the size of the sectional shape of a parallelbeam from the laser 112 into a desired value (for example, by changingthe sectional shape from a rectangle to a square), thus reshaping thebeam shape to a desired one. The beam shaping system 114 forms a beamthat has a size and a divergent angle necessary for illuminating anoptical integrator 118 described later.

The illumination optical system is an optical system that illuminatesthe mask 130. The illumination optical system includes, in the instantembodiment, a condensing optical system 116, a polarization controller117, the optical integrator 118, an aperture stop 120, a condenser lens122, a deflecting mirror 124, a masking blade 126, and an imaging lens128. The illumination optical system can realize various illuminationmodes, such as a conventional illumination, an annular illumination, aquadrupole illumination, a hexapole illumination described later, etc.

The condensing optical system 116 includes plural optical elements, andefficiently introduces a beam with the desired shape into the opticalintegrator 118. For example, the condensing optical system 116 involvesa zoom lens system to control the shape and an angular distribution ofthe incident beam to the optical integrator 118.

The condensing system 116 further includes an exposure dose adjustingpart that can change an exposure dose of the illumination light for themask 130 per illumination. The exposure dose adjusting part iscontrolled by the main control unit 150. An exposure dose monitor may beplaced between the optical integrator 118 and the mask 130 or anotherplace to measure the exposure dose, and the measurement result may befed back.

The polarization controller 117 includes, for example, a polarizationelement at an approximately conjugate to a pupil 142 of the projectionoptical system 140. The polarization controller 117 controls, asdescribed later, a polarization state in a predetermined region in aneffective light source formed on the pupil 142. The polarizationcontroller 117 includes plural types of polarization elements that areprovided on a turret rotatable by an actuator (not shown), and the maincontrol unit 150 controls a driving of the actuator.

The optical integrator 118 forms uniform illumination light thatilluminates the mask 130, includes a fly-eye lens in the instantembodiment for converting the angular distribution of incident lightinto a positional distribution, and exits the light. However, theoptical integrator 118 usable for the present invention is not limitedto the fly-eye lens, and can include an optical rod, a diffractionoptical element, and a micro-lens array etc.

Provided right after an exit plane of the optical integrator 118 is theaperture stop 120 that has a fixed shape and diameter. The aperture stop120 is arranged at a position approximately conjugate to the pupil 142of the projection optical system 140 as described later, and an apertureshape of the aperture stop 120 defines a shape of the effective lightsource on the pupil 142 plane in the projection optical system 140. Theaperture stop 120 controls, as described later, the shape of theeffective light source.

Various aperture stop described later can be switched so that it islocated on an optical path by a stop exchange mechanism (or actuator)121 according to illumination conditions. A drive control unit 151controlled by the main control unit 150 controls a driving of theactuator 121. The aperture stop 120 may be integrated with thepolarization controller 117.

The condenser lens 122 condenses plural beams that have exited from asecondary light source near the exit plane of the optical integrator 118and passed the aperture stop 120. The beams are reflected by the mirror124, and uniformly illuminate or Koehler-illuminate the masking blade126 plane as a target surface.

The masking blade 126 includes plural movable shielding boards, and hasa rectangular opening shape corresponding to a shot area of theprojection optical system 140. The masking blade 126 is a stop having anautomatically variable opening width. Moreover, the exposure apparatus100 further includes a stop having a slit shape opening, and the stop isarranged near the masking blade 126.

The imaging lens 128 images the opening shape of the masking blade 126onto the mask 130 plane.

The mask 130 has the pattern to be transferred, and is supported anddriven by a mask stage 132. FIG. 4A shows an example of the maskpattern. Here, FIG. 4A is a plane view of one example of a contact holepattern formed on the mask 130. A detailed description will be given ofthe pattern later. A diffracted light emitted from the mask 130 isprojected onto the substrate 170 by the projection optical system 140.The substrate 170 includes a wafer 174 and a photoresist 172 that isapplied onto the wafer 174. The mask 130 and the substrate 170 arearranged in an optically conjugate relationship. The exposure apparatus100 is the step-and-scan manner exposure apparatus (i.e., scanner), andscans the mask 130 and the substrate 170 to transfer the pattern of themask 130 onto the substrate 170. When the exposure apparatus 100 is thestep-and-repeat manner exposure apparatus (i. e., stepper), the mask 130and the substrate 170 are kept stationary during exposure.

The mask stage 132 supports the mask 130, and is connected to a movingmechanism (not shown). The mask stage 132 and the projection opticalsystem 140 are installed on a stage barrel stool supported via a damper,for example, to a base frame placed on the floor. The mask stage 132 canuse any structure known in the art. The moving mechanism (not shown) ismade of a liner motor and the like, and can move the mask 130 by drivingthe mask stage 132 in X-Y directions. The exposure apparatus 100synchronously scans the mask 130 and the substrate 170 under control bythe main control unit 150.

The projection optical system 140 serves to image the diffracted lightthat has been generated by the pattern of the mask 130 onto thesubstrate 170. The projection optical system 140 may use a dioptricoptical system including a plurality of lens elements, and acatadioptirc optical system including a plurality of lens element and atleast one concave mirror, etc.

The main control unit 150 controls driving of each component, andparticularly controls the illumination based on information input into amonitor and input device 152, information from the illuminationapparatus 110, and a program stored in a memory (not shown). Morespecifically, the main control unit 150 controls, as described later,the shape and polarization state of the effective light source formed onthe pupil 142 of the projection optical system 140. Control informationand other information for the main control unit 150 are indicated on adisplay of the monitor and input device 152.

The wafer 174 is replaced with a liquid crystal plate in anotherembodiment.

The wafer 174 is supported by a wafer stage 176. The wafer stage 174 mayuse any structure known in the art, and thus a detailed description ofits structure and operations is omitted. For example, the wafer stage176 uses a liner motor to move the wafer 174 in X-Y directions. The mask130 and the wafer 174 are, for example, scanned synchronously, and thepositions of the mask stage 132 and the wafer stage 176 are monitored,for example, by a laser interferometer and the like, so that both aredriven at a constant speed ratio. The wafer stage 176 is installed on astage stool supported on the floor and the like, for example, via adumper.

The liquid 180 uses, for example, a pure water.

Hereinafter, referring to FIGS. 2B and 4A. a description will be givenof a basic example of a mask pattern MP₁. Here, FIG. 2B is a plane viewof the basic example of the mask pattern MP₁. The mask pattern MP₁, asshown in FIG. 2B, consists of holes so that the centers of the holes maymake triangular grids. FIG. 2B shows a binary mask. In the mask patternMP₁, the contact hole CH₁ and the contact hole CH₂ are lighttransmitting part, and LS is light shielding part.

FIG. 4A is a plane view of contact hole pattern MP₂ is an aggregate ofthe hole pattern MP₁. In FIG. 4A, W is a width of the contact hole CH,Px is a pitch in X direction, and Py is a pitch in Y direction. Acontact hole array comprises a plurality of periodic patterns having thepitch Px in X direction (first direction). The plurality of periodicpatterns are arranged in Y-direction (second direction) while shiftingby half a pitch (Px/2) to an upper and lower contact hole arrays, andthe centers of the contact holes may make triangular grids.

In the binary mask, the contact hole CH (white portion) is the lighttransmitting part with a transmittance of 1, and the background (blackportion) is the light shielding part LS with a transmittance of 0. Inthe attenuated phase shift mask, the hole (white part) is thetransmitting part with a transmittance of 1, the background (blackportion) is a half shielding part with a transmittance of approximately6%, and a phase of the background (black portion) inverts by 180 degreesto a phase of the hole portion (white part). In an alternated phaseshift mask, such a pattern cannot be arranged as described later.

The pitch Px in X-direction and the pitch Py in Y-direction arenormalized by λ/NA, and the pitches Px and Py is determined to satisfythe following expressions.Pxo/2=(Px/2)NA/λ  (2)Pyo/2=(Py/2)NA/λ  (3)1/(4(Pyo/2))/sin(2α)>1  (4)(½(Pyo/2))/sin(tan⁻¹(2sin(2α)))<1  (5)

In particular, if Pitch Py is Py=√{square root over ( )}3Px/2, then acertain hole is equal distance to six neighboring holes, and thetriangular grid pattern. In this case, a half pitch of the pattern(Px/2) is determined by the following expression.0.33λ/NA<Px/2<0.67λ/NA  (6)

If the half pitch of the pattern is determined, the NA of the projectionoptical system satisfied the following expression, where P is the pitch.0.33λ/(P/2)<NA<0.67λ/(P/2)  (7)

If the isolated pattern is formed, six auxiliary patterns AP arearranged around the target pattern (isolated pattern) CH as shown inFIG. 20 by the methods disclosed in Japanese Patent Applications,Publication Nos. 2004-272228 and 2003-318100. In FIG. 20, S is a lengthof one side of the auxiliary pattern AP, and W is a length of one sideof the target pattern CH. FIG. 20 shows the target pattern CH as a whitepattern and the auxiliary pattern AP as a gray pattern. In this case, anexposure condition is set so that the target pattern CH is resolved andthe auxiliary pattern is prevented from being resolved. If a pitch in alateral direction is Px and a pitch in a longitudinal direction is Py,the pitch Px is set to the range of the expression (6). In other words,if a standardized value of the half pitch (Px/2) by λ/NA is k₁, k₁ isset to 0.33<k₁<0.67. Therefore, all pitches between the holes that arePy=√3Px/2 is Px/2, and the triangular grid pattern.

When the six auxiliary patterns AP cannot be arranged because otherpatterns exist, the auxiliary patterns AP are arranged so that thetriangle is formed as shown in FIGS. 21A to 21D. Here, FIGS. 21A to 21Dare schematic plane views of an insertion method of the auxiliarypatterns to the isolated pattern. The width S of the auxiliary patternAP may be 0.6 times to 0.8 times of the half pitch Px/2 of the targetpattern CH to prevent the resolution of the auxiliary pattern AP.Generally, a size of the auxiliary pattern AP is 0.6 times to 0.8 timesof the half pitch of the auxiliary pattern AP or 0.6 times to 0.8 timesof a size of the isolated contact hole CH. Even when the isolatedpatterns with a different size are exposed at the same time, all thehalf pitches of the auxiliary patterns are set to equal.

FIG. 2A is a schematic plane view of an aperture stop 120A that isconfigured as a stop for the hexapole illumination applicable to theaperture stop 120. The aperture stop 120A includes six circles with a σof 0.2 or less at a center. Here, the σ is a value that divides thenumerical aperture of the illumination optical system by the numericalaperture of the illumination optical system 140, and corresponds to asize of diameter of the illumination light on the pupil plane in theprojection optical system 140 when a diameter of pupil of the projectionoptical system 140 is 1.0. The aperture stop 120A includes atransmitting part 121 a (white portion) with a transmittance of 1 havingsix circles and a shielding part 121 b (gray portion) with atransmittance of 0. The effective light source is arranged as shown inFIG. 2A to the contact hole pattern MP shown in FIG. 2B. A centerposition (center of gravity position) of one pole of such a hexapoleeffective light source is expressed by the following expressions.α=tan⁻¹(Pxo/(2Pyo))  (8)a=1/(4(Pyo/2)/sin(2a))  (9)

a is a distance from a pupil center (an optical axis of the projectionoptical system 140) to the center position of each pole 121 a, and isequal to each pole. As above-described, a direction from the pupilcenter to the center position of each pole 121 a is 0, 2α, π−2α, π,π+2α, and 2π−2α, when X-direction is a standard. Particularly, when thepitch Py is determined to Py=√3Px/2, the half pitch (Px/2) is expressedby the following expression using k₁.Px/2=k1(λ/NA)=Pxo/2(λ/NA)  (10)

The center positions of each pole of hexapole are near1/(3(Pxo/2))=1/(3k₁), and are arranged in directions of 0 degree, 60degrees, 120 degrees, 180 degrees, 240 degrees, and 300 degrees whenX-direction from the optical axis is a standard. In this case, adirection to circumference contact hole patterns centering on thecertain contact hole pattern accords with a direction to each pole ofhexapole from the optical axis of the projection optical system 140.

Although a shape of each pole 121 a of hexapole is circle in FIG. 2A, itmay be an arc or a sector. Preferably, center positions of six poles area rotational symmetry shape to the optical axis of the projectionoptical system 140.

As shown in FIG. 16A, when the direction from the optical axis to eachpole of hexapole accords with the direction to the circumference contacthole patterns centering on the certain contact hole pattern of the basicpattern shown in FIG. 2B, the expression (8) is not satisfied. Here,FIG. 16A is a schematic plane view of an aperture stop that isconfigured as a stop for the hexapole illumination inapplicable to theaperture stop 120. If the expression (8) is not satisfied as shown inFIG. 16A, an imaging performance deteriorates. The fine patterngenerates a two beam interference that interferences only two beam of0^(th) diffracted light and 1^(th) diffracted light from the pattern asshown in FIG. 16B. Even if the pattern is large, a four beaminterference that interferences four beam of 0^(th) diffracted light andthree 1^(th) diffracted light from the pattern is generated as shown inFIG. 16C, and a three beam interference is not realized. Here, FIG. 16Bis a schematic plane view of an example that generates the two beaminterference when the direction from the optical axis to each pole ofhexapole does not accords with the direction to the circumferencecontact hole patterns centering on the certain contact hole pattern.FIG. 16C is a schematic plane view of an example that generates the fourbeam interference when the direction from the optical axis to each poleof hexapole does not accords with the direction to the circumferencecontact hole patterns centering on the certain contact hole pattern. Thecontrast in one direction is only good and the contrast in theorthogonal direction is low in the two beam interference, a sufficientdepth of focus is not obtained in the four beam interference that isasymmetrical to the pupil center shown in FIG. 16C, and the imagingperformance degradates than the three beam interference.

Where a is a center position of each pole in a pupil coordinate system(or a distance in a radial direction from an origin in the pupilcoordinate system).

Where α is a central angle of each pole in the pupil coordinate system(or a central angle from a X-axis in the pupil coordinate system).

Hereinafter, referring to FIGS. 17A and 17B, a description will be givenof a reason that the phase shift mask is not desirable to the mask 130.Here, FIG. 17A is a schematic plane view of a phase shift mask thatincludes a matrix contact hole pattern MP₁₀. The phase shift maskcancels 0^(th) diffracted light by inverting the phase of light thattransmits the adjacent transmitting parts on the mask by 180 degrees,and images by interfering two beam of ±1^(th) diffracted light. Thistechnology can substantially set k₁ of the above expression to 0.25 tothe resolution of line and space (L & S) in one direction, can improvethe resolution R, and can form the pattern of 0.1 μm or less on thewafer.

The pattern MP₁₀ includes, as the light transmitting part that invertsthe phase of light from the adjacent transmitting part by 180 degrees,contact hole patterns CH₁₀ and CH₁₁ with a width W (nm) are periodicallyarranged at a pitch P (nm) in the light shielding part LS, such aschromium. FIG. 17A shows the light shielding part LS by a black portionand the light transmitting parts CH₁₀ and CH₁₁ by a white portion andgray portion, and the gray portion CH₁₁ has a phase that inverted aphase of the white portion CH₁₀ by 180 degrees.

FIG. 17B shows diffracted light from the mask pattern MP₁₀. In FIG. 17B,1^(th) diffracted light shown by a black dot is generated. Althoughdiffracted light shown by a white dot is generated in the binary mask,0^(th) diffracted light disappears and 1^(th) diffracted light has apitch of half of the binary mask in the phase shift mask. If a length ofhalf pitch is k₁, although the pattern to k1=0.25√2=0.358 passes thepupil, the pattern with a length of the half pitch smaller than thisdoes not pass the pupil (see, Japanese Patent Application, PublicationNo. 2000-040656). A resolvable pattern is until a fine pattern of √2that is a resolution limit of line and space (L & S).

When the phase shift mask shown in FIG. 17A is illuminated by theillumination light that forms the circular effective light source ofσ=0.2 shown in FIG. 18 a using ArF excimer laser and the immersionexposure apparatus with a NA of 1.35, the contrast changes as shown inFIG. 19A according to a change of the length of the half pitch, and thedepth of focus changes as shown in FIG. 19B. The length of the halfpitch is k₁, and a unit of the depth of focus is μm. The depth of focusis a range that can obtain the contrast of 40% or more and tolerates achange of ±10% of the width of contact hole from 0.9 times to 1.1 timesto the predetermined width W.

In this case, the half pitch that can obtain 40% or more of contrast isk₁>0.37, and the contrast is good in a larger half pitch than this.However, the depth of focus is almost 0.15 μm to 0.2 μm, and is notadapted for a mass production. If the half pitch is k₁=0.50 or more, thehalf pitch of 0.3 μm or more necessary for the mass production can beobtained. Thus, although the image by the four beam interference hashigh contrast, the half pitch with k₁=0.50 or more is necessary toobtain a practical depth of focus.

On the other hand, a method for the resolution of contact hole sequenceto k₁=0.25, as an overlay of a longitudinal line and a lateral line inthe resolution limit of L & S, has proposed to obtain the resolution ofcontact hole sequence similar to the resolution of L & S. See, forexample, Japanese Patent Applications, Publication Nos. 2000-040656 and2003-203850. This method forms the longitudinal line by the two beaminterference and the lateral line by the two beam interference, andforms the contact hole sequence by a trellis pattern that overlaysthese. However, even if the longitudinal line and the lateral line isoverlaid, since the contrast becomes only 0.5 at the maximum, it is hardto obtain an exposure tolerance and is not practical.

The three beam interference proposed in the instant embodiment solvesthis problem. Hereinafter, a description will be given of a method thatresolves the contact hole pattern using the three beam interference.FIG. 4B shows a position of diffracted light from checker contact holepattern MP₂ shown in FIG. 4A. Six 1^(th) diffracted lights aredistributed around 0^(th) diffracted light as shown in FIG. 4B.

FIG. 4B is a diffracted light distribution from the binary mask, andshows an amplitude of diffracted light from the contact hole patternwith a contact hole width W of 80 (nm) and pitches Px and Py of 160 (nm)as shown in FIG. 4A. However, even if the mask is the attenuated phaseshift mask, the pattern of diffracted light does not change but only anamplitude ratio between 0^(th) diffracted light and 1^(th) diffractedlight is different. As reference, a size of the pupil is shown in FIG.4B by a white circle when the NA of the projection optical system is1.35. The standardized value of the half pitch of 80 (nm) by λ/NA, inother words, k₁ is 0.56.

Here, when the pupil is shifted so that three beam enter the pupil,diffracted light is shown in FIG. 5. If the light inclines in threedirections, three lights symmetrically enters as shown in FIG. 5. Then,if the image obtained from each is incoherent-added, the contact holewith high contrast is obtained. For this reason, the effective lightsource is the hexapole illumination as shown in FIG. 2, and the threebeam interference is formed in six directions. Six 1^(th) diffractedlights B to G are distributed around a 0^(th) diffracted light A. Thediffracted lights A to B interfere (three beam interference) in a firstpupil, the diffracted lights A, C and D interfere in a second pupil, thediffracted lights A, D and E interfere in a third pupil, the diffractedlights A, E and F interfere in a fourth pupil, the diffracted lights A,F and G interfere in a fifth pupil, and the diffracted lights A, B and Ginterfere in a sixth pupil.

In the three beam interference, the three beam should symmetricallyenter to the center position of the pupil to obtain the depth of focus.If a defocus generates, a wave front corresponds to a square of adistance from the pupil center. Therefore, if the three beamsymmetrically enter to the center position of the pupil, a phasedifference from a defocus wave front is lost (becomes 0). Thereby, whenthe defocus generates, a degradation of image becomes the minimum.

A description will be given of the three beam interference of thediffracted lights A to C on the pupil shown in FIG. 6. In a condition onwhich distances a, b and c from the center are equal, if a middle pointof BC is L, an angle between AB and AL is equal to an angle between ABand AO, a triangle ABC is equal to a triangle A′B′C′, and an anglebetween AB and AL is equal to an angle between AB and BL′ because AL isparallel to BL′. Therefore, if the angle between AB and AL is α, thefollowing expression is materialized.AL=A′L′=1/Px  (11)BC=B′C′=1/Py  (12)α=tan ⁻¹(Px/(2Py))  (13)b sin(2α)=1/(2Py)  (14)a=b=c=1/(2Py)/sin(2α)  (15)

In the three lights A, B and C, if the center position of the pupil islocated on a point O, distances A, B and C of the three lights becomeequal. To locate the center position of the pupil in the point O, theexpressions 8 and 9 are satisfied so that 0^(th) diffracted lightseparates from the center position of the pupil by a. If the directionof each pole of the hexapole is satisfied the above explained, thesymmetry of the pattern becomes good. However, even if the directionshifts little, the pattern is resolved.

The minimum radius to enter the three lights to the pupil is expressedby the following expression.a=b=c=1/(2Py)/sin(2α)<1  (16)

The maximum radius to enter the three lights to the pupil is a radiussmaller than a dotted line of FIG. 6B. For example, a point O′ islocated on the center as shown in FIG. 6B in other light source of thelight source that the point O is located on the center, anda=b=c=a′=b′=c′ is satisfied. When the maximum radius is smaller than thedotted line, only three lights enter the pupil. However, the maximumradius is larger than the dotted line, diffracted lights of four or morelights enter the pupil, and the degradation of defocus becomes large.Therefore, the following expression is satisfied.d=e=(1/Py)/sin(tan⁻¹(1/Py/a))=(1/Py)/sin(tan⁻¹(2 sin(2α)))<1  (17)

For example, when the pitch of the pattern is Px=Py=Pz and the halfpitch of the pattern is k₁, the center position of the light source is1/(3.2k₁). If the directions of each pole of the hexapole illuminationare 53 degrees, 127 degrees, 180 degrees, 233 degrees and 307 degrees,the symmetry of the pattern becomes good. In this case, the minimumresolution satisfies the following expressions from 1/(3.2k₁)<1.k₁>0.3125  (18)0.3125<k₁<0.5896  (19)

Therefore, when the size of the pupil (NA) is determined, the half pitchof the pattern is 0.31 k₁<0.59. When the half pith of the pattern isdetermined, the size of the pupil (NA) preferably satisfies thefollowing expression.0.31λ/(P/2)<NA<0.59λ/(P/2)  (20)

Particularly, if the pitch of Py is determined to Py=√3Px/2, thetriangular grid pattern that the six holes are arranged around onecertain contact hole at pitch Px. In this case, the three lights becomesthe equilateral triangle, if the three lights is symmetrically imaged tothe pupil center, the depth of focus can be further obtained.

In the three beam interference, the number of contact holes integratedwithin the wafer plane is most numbers in this case. The half pitch ofthe pattern in the lateral direction is Px/2, all of half pitchesbetween the holes are Px/2, and the equilateral triangle with AB=BC=CAis formed. If Px/2 is k₁, the following expressions are satisfied.AB=BC=CA  (21)a=b=c=1/(3k₁)  (22)

Therefore, the center position of the light source is 1/(3k₁). Theminimum radius to enter the three lights to the pupil is expressed bythe following expressions.a=b=c=1/(3k₁)<1  (23)k₁>0.3333  (24)

In the maximum radius to enter the three lights to the pupil, thefollowing expressions are satisfied.d=e=(1/Py)/sin(tan⁻¹(2 sin(2α)))<1  (25)(1/(√3k₁))/0.866<1  (26)k₁<0.667  (27)

Therefore, 0.33<k₁<0.67 is satisfied. If the pitch is P, the followingexpression is satisfied from k₁λ/NA.0.33λ/(P/2)<NA<0.67λ/(P/2)  (28)

Since the minimum resolution in the four beam interference is k₁>0.25√2=0.358, the resolution in the three beam interference is better thanthe resolution in the four beam interference. If the resolution limit issimply compared, the integrated degree improves by about 1.3 times.

Hereinafter, a description will be given of a polarization state of thethree beam interference. In the immersion exposure apparatus, theimmersion exposure apparatus with a NA of 1.35 is planned. A refractiveindex of water is about 1.44. In an optical system with a NA of 1.35, ifan incident angle is θ, θ is 70 degrees from NA=n sin θ and n=1.44. Inan oblique incidence illumination with the incident angle of 70 degrees,the fine pattern near the resolution limit of the optical systeminterferes at the maximum incident angle, and a coherence decreasesaccording to the polarization state. Therefore, the illumination lightneeds to have a good polarization direction of the coherence.

When the mask 130 is the attenuated phase shift mask, the polarizationdirection of the illumination light preferably is a polarization in aradial direction as shown in FIG. 3A. Here, FIG. 3A is a schematic planeview of the polarization direction of the illumination light when themask 130 is the attenuated phase shift mask. The diffracted light fromthe mask 130 ideally has the same polarization direction as the incidentlight, and the polarization direction of 0^(th) diffracted light and thepolarization directions of six 1^(th) diffracted lights around it arethe same.

FIG. 3B shows a polarization state of the three beam in a polarizationstate of two light sources S1 and S5 among six light sources S1 to S6 ofthe hexapole illumination shown in FIG. 3A.

In one light source S5 of the hexapole illumination, 0th diffractedlight A and 1th diffracted lights B and C interferes as shown in FIG.3B.

The diffracted lights A, B and C have the polarization direction shownin FIG. 3 by the radial polarization, and a coherence between A and C, acoherence between A and B and a coherence between B and C are good.

Particularly, in the attenuated phase shift mask, although the 0thdiffracted light A is different from the 1th diffracted lights B and Cin sign and size of amplitude, the coherence between B and C isimportant because B and C are the same.

In the attenuated phase shift mask, the polarization directions of thediffracted lights A, B and C rotates by 90 degrees by the tangentialpolarization, the contrast decreases because the coherence between thediffracted light B and the diffracted light C decreases.

In the binary mask, the polarization direction of the illumination lightpreferably is the tangential polarization as shown in FIG. 3C. Here,FIG. 3C is a schematic plane view of the polarization direction of theillumination light when the mask 130 is the binary mask. FIG. 3D shows apolarization state of two light sources S1 and S5 among six lightsources S1 to S6 of the hexapole illumination shown in FIG. 3C. Sincethe 0^(th) diffracted light A and 1^(th) diffracted light B and C arethe same sign of amplitude, the coherence between the diffracted light Aand the diffracted light B and the coherence between the diffractedlight A and the diffracted light C is better than the coherence betweenthe diffracted light B and the diffracted light C and can obtain thecontrast. In the binary mask, since a difference by polarization is notso large, the illumination light may be an unpolarized light. If theillumination light is the unpolarized light, the binary mask can obtainhigher contrast than the attenuated phase shift mask.

First Embodiment

The pitches in the longitudinal direction and the lateral direction arethe same (Px=Py=P), and the contrast and the depth of focus is shownwhen the contact hole is imaged changing the pitches using the ArFexcimer laser with a wavelength of 193 nm and the immersion exposureapparatus 100 with a NA of 1.35. The refractive index is about 1.44. Themask 130 uses the attenuated phase shift mask.

A change of the contrast by the polarization direction was investigated.The effective light source is the hexapole illumination as shown in FIG.2A, σ is 0.80, and a size of a local light source is σr=0.10. The radialpolarization shown in FIG. 3A, the tangential polarization shown in FIG.3B and the unpolarized light are compared as the polarization.

FIG. 7 is a graph of this result. In FIG. 7, a lateral axis is the halfpitch of the contact hole (nm), and a longitudinal axis is a contrastpeak. The contact hole width W is W=P/2 and Px=Py=P. Referring to FIG.7, the radial polarization obtains high contrast.

Moreover, σr of the effective light source is fixed to 0.10, σ is use asa parameter and the change of the contrast was investigated changing thehalf pitch. The polarization direction is the radial polarization. FIG.8 is a graph of this result. The contrast of 40% or more can be obtaineduntil near 0.35k₁ to finer half pitch. Similarly, σr of the effectivelight source is fixed to 0.10, σ is use as a parameter and the change ofthe depth of focus was investigated changing the half pitch. Thepolarization direction is the radial polarization. FIG. 9 is a graph ofthis result.

In exposure, an error of exposure dose and a focus setting error are notavoided, but the contact hole must be formed on the image plane withinan error tolerance. Moreover, the contrast of 40% or more is required toexpose the resist. The error of exposure dose is estimated to 5%, and afocus range that the size of the contact hole pattern on the image planepermits the change of less than 10% to a predetermined contact holewidth and satisfies the contrast of 40% or more is defined as thepractical depth of focus. In other words, if the predetermined contacthole width is W to the change of 5% of exposure dose, the focus rangethat the width of the contact hole on the image plane is 90% or more and110% or less and satisfies the contrast of 40% or more is defined as thedepth of focus. In three beam exposure, large depth of focus isobtained, and the depth of focus of 0.3 μm or more is obtained untilnear to 0.4k₁ half pitch.

Even if the mask pattern is the same, unless the effective light sourceis suitable, the depth of focus is not obtained.

A description will be given of a small σ illumination shown in FIG. 18Aand an annular illumination shown in FIG. 18B as an example. The contacthole with W=80 (nm) and Px=Py=P=80 (nm) as shown in FIG. 4A is exposedusing the exposure apparatus 100 (ArF excimer laser, NA=1.35). Theeffective light source uses the small σ illumination (σ=0.3) shown inFIG. 18A and the annular illumination (outside σ=0.65, inside σ=0.45)shown in FIG. 18B. Both are an unpolarized light illumination. These anda case that the contact hole is exposed using the hexapole illuminationshown in FIGS. 2A and 3A are compared. The half pitch of the pattern is80 nm (k₁=0.56). The illumination condition is outside σ=0.65, localσr=0.1, center position 1/(3.2*0.56)=0.55−. In this case, to thedefocus, the contrast and the size of the contact hole (CriticalDimension: CD) change as shown in FIGS. 10 and 11. In the small σillumination, although the most high contrast image is obtained, thefocus range to obtain the contrast of 40% or more does not have even 0.2μm, a CD change to the defocus is large, and the depth of focus is notobtained. The annular illumination obtains larger depth of focus thanthe small σ illumination but the depth of focus is smaller than 0.2 μm.

In the small σ illumination, since the light enters almostperpendicularly, seven lights of 0^(th) diffracted light and six 1^(th)diffracted lights interfere. Therefore, although the high contrast canbe obtained in the best focus, the depth of focus cannot be obtained. Inthe annular illumination, the light enters by oblique incidence andthree beam interfere. However, since three beam include many lights thatare not symmetry to the center of the pupil, the degradation of theimage to the defocus becomes large and the depth of focus is notobtained. On the other hand, in the hexapole illumination that includesthree beam that are symmetry to the center of the pupil, the degradationof the image to the defocus is little, and large depth of focus isobtained.

Second Embodiment

The pitches in the longitudinal direction and the lateral direction arethe same (Px=Py=P), and the contrast and the depth of focus is shownwhen the contact hole is imaged changing the pitches using the ArFexcimer laser and the immersion exposure apparatus 100 with a NA of1.35. The refractive index is about 1.44. The mask 130 uses the binarymask.

A change of the contrast by the polarization direction was investigated.The effective light source is the hexapole illumination as shown in FIG.2A, σ is 0.80, and a size of a local light source is σr=0.10. The radialpolarization shown in FIG. 3A, the tangential polarization shown in FIG.3B and the unpolarized light are compared as the polarization.

FIG. 12 is a graph of this result. In FIG. 12, a lateral axis is thehalf pitch of the contact hole (nm), and a longitudinal axis is acontrast peak. The contact hole width W is W=P/2 and Px=Py=P. Referringto FIG. 12, the tangential polarization obtains high contrast in thebinary mask. However, the difference of the polarization by thepolarization is little. The same contrast when the radial polarizationilluminates (polarization in the radial direction) the attenuated phaseshift mask (FIGS. 7 and 8, etc.) is obtained by any polarizationdirection.

Moreover, the effective light source is fixed to σ=0.80 and the size ofthe local light source is fixed to σr=0.10, and the change of the depthof focus was investigated changing the half pitch. The radialpolarization, the tangential polarization and the unpolarized light arecompared as the polarization. FIG. 13 is a graph of this result. In thebinary mask, referring to FIG. 13, the tangential polarization obtainsthe depth of focus better than other polarization states in the finehalf pitch. However, the difference of the depth of focus by thepolarization direction is little. The depth of focus is almost same byany polarization direction.

Third Embodiment

Next, a description will be given of the depth of focus when the pitchof Py is determined to Py=√3Px/2. The contact hole width W is W=Px, andPy=√3Px/2. The contrast and the depth of focus is shown when the contacthole is imaged changing the pitches using the ArF excimer laser and theimmersion exposure apparatus 100 with a NA of 1.35. The refractive indexis about 1.44. The mask 130 uses the attenuated phase shift mask.

The effective light source is the hexapole illumination as shown inFIGS. 2A and 3A, and a size of a local light source is σr=0.10. Thepolarization is the radial polarization shown in FIG. 3A to obtain highcontrast from the result of the first embodiment.

In FIG. 14, σr of the effective light source is fixed to 0.10, σ is useas a parameter and the change of the contrast was investigated changingthe half pitch. A lateral axis is the half pitch of the contact hole(nm), and a longitudinal axis is a contrast peak. The contrast of 40% ormore can be obtained until near 0.35k₁ to finer half pitch. The goodcontrast is obtained in the fine pitch than the result of the firstembodiment.

Similarly, σr of the effective light source is fixed to 0.10, σ is useas a parameter and the change of the depth of focus was investigatedchanging the half pitch. FIG. 15 is a graph of this result. Thepolarization direction is the radial polarization. Three light exposureobtains large depth of focus and obtains the depth of focus of 0.3 μm ormore until near 0.35k₁ to finer half pitch. The larger depth of focusthan the first embodiment can be obtained.

Fourth Embodiment

The instant embodiment uses the attenuated phase shift mask as the mask130, and exposes the isolated contact hole CH. In the isolated contacthole CH, the auxiliary pattern AP is arranged around the hole so thatthe triangle is formed and six auxiliary patterns AP are arranged in theisolated hole. As shown in FIGS. 23A to 23E, the auxiliary pattern AP issequentially added around the isolated contact hole CH so that theauxiliary pattern AP forms the triangle. An auxiliary pattern is placedsymmetrical to the target pattern. Then, the six auxiliary patterns APare inserted around the isolated contact hole pattern CH as shown inFIG. 22.

An isolated contact hole pattern CH₄ that does not have the auxiliarypattern shown in the upper right of FIG. 22 is compared with an isolatedcontact hole pattern CH₃ that has six auxiliary patterns AP shown in thelower left of FIG. 22. A size of the auxiliary pattern AP is a width s.If the pitch in the lateral direction is Px and the pitch in thelongitudinal direction is Py, then Px is set to 0.33<k₁<0.67 using k₁ asthe half pitch of the pattern (Px/2) and Py is set to Py=√3Px/2. CHshows CH₃ and CH₄.

The isolated contact hole CH with a size of W=72 (nm), the isolatedcontact hole CH with a size of 79 (nm), the isolated contact hole CHwith a size of 86 (nm) and the isolated contact hole CH with a size of100 (nm) are resolved at the same time. Since only the isolated contacthole CH exists, the half pitch of the auxiliary pattern AP is arbitraryin the range of 0.33<k₁<0.67. However, a constant half pitch is setirrespective of the size of the isolated contact hole CH to set theoptimal exposure condition. In this case, all half pitches are set toP/2=72 (nm).

The ArF excimer laser and the immersion exposure apparatus 100 with a NAof 1.35 are used, and the half pitch is k₁=0.5 using k₁. The effectivelight source is the hexapole illumination as shown in FIGS. 2A and 3A,and a size of a local light source is σr=0.10. The polarization is theradial polarization shown in FIG. 3A to obtain high contrast from theresult of the first embodiment. The center position of hexapole is1/(3k₁)=0.67. All sizes of auxiliary patterns S are the same, and are0.8 times of the half pitch, in other words, S=0.80·P/2=58 (nm). FIG. 24shows a result of a two-dimension intensity distribution in this case,and shows intensity with a predetermined intensity and a level contourline of ±20% to its intensity. In FIG. 24, an upper shows the best focusand a lower shows ±0.1 μm defocus.

The contrast of the isolated contact hole CH₃ is better than thecontrast of the isolated contact hole CH₄, and the hole pattern is alsoobtained in the defocus. Therefore, the holes of these different sizesare formed in the depth of focus to 0.2 μm. Thus, the size of theauxiliary pattern AP is 0.6 times to 0.8 times of the half pitch of theauxiliary pattern AP or 0.6 times to 0.8 times of the isolated contacthole pattern CH. However, when the isolated contact hole patterns CHwith different sizes are exposed at the same time, all half pitches ofthe auxiliary patterns AP may be set to the same and the size of theauxiliary pattern AP may be set to 0.6 times to 0.8 times of the halfpitch of the auxiliary pattern AP. When the size of the hole patterndiffers, the size is corrected so that the size becomes thepredetermined size in the same exposure dose.

Fifth Embodiment

The instant embodiment uses the attenuated phase shift mask as the mask130 and the isolated pattern and dense pattern are included as shown inFIG. 25. an isolated pattern CH₅ does not includes the auxiliary patternto compare. an arrangement of the auxiliary pattern AP as shown in FIG.25 can be considered. When the auxiliary pattern cannot be arrangedsince target pattern and other pattern are close, the auxiliary patternis arranged around the target pattern so that the triangle is formed asshown in FIGS. 21A to 21D. The pitches Px and Py of the auxiliarypattern AP are accorded with the minimum pitch of the dense pattern.

The auxiliary pattern is arranged around the outer hole in the densepattern so that the triangle is formed, similarly the isolated hole.

The size is corrected so that dense hole and isolated hole becomes samesize in the same exposure dose. In the dense hole, if the size iscorrected so that a center and outer hole become same size in the sameexposure dose, an uniformity of the size of the congestion patternbecomes still better. However, the size of the outer-hole is notcorrected in the instant embodiment.

The exposure result of hole with w=72 (nm) and half pitch (Px/2) of 72(nm) is shown using the mask pattern of FIG. 26 as the target pattern ofFIG. 25. The half pitch of the auxiliary pattern is set to the same asthe half pitch (Px/2=72, Py=√3Px/2) of the dense pattern. Although thesize of the hole of the dense pattern is 72 (nm), the size of theisolated hole is set to Wi=72 * 1.06=76 (nm) and the width of theauxiliary pattern is set to S=W_(i) * 0.75=57 (nm) that the size of thehole of the dense pattern is the same as the size of the isolated hole.In this case, the exposure condition is the same as the fourthembodiment.

FIG. 28 shows a two-dimension intensity distribution as an exposureresult, and shows intensity with a predetermined intensity and a levelcontour line of ±20% to its intensity. The size of the hole of the densepattern and the isolated hole becomes uniformly, and it is resolved in±0.1 μm defocus shown in right side.

Next, the exposure result of further fine hole with w=65 (nm) and halfpitch (Px/2) of 65 (nm) is shown using the mask pattern of FIG. 26 asthe same target pattern of FIG. 25. Although the size of the hole of thedense pattern is 65 (nm), the size of the isolated hole is set toWi=65 * 1.20=78 (nm) and the width of the auxiliary pattern is set toS=Wi * 0.75 =58 (nm) so that the size of the hole of the dense patternis the same as the size of the isolated hole. If it is exposed by theArF excimer laser and the immersion exposure apparatus with a NA of1.35, the half pitch becomes k₁=0.45 using k₁ as the half pitch. Theeffective light source is the hexapole illumination as shown in FIGS. 2Aand 3A, and a size of a local light source is σr=0.10. The polarizationis the radial polarization shown in FIG. 3A to obtain high contrast fromthe result of the first embodiment. The center position of the hexapoleis 1/(3k₁)=0.74.

FIG. 29 shows a two-dimension intensity distribution as an exposureresult. The size of the hole of the dense pattern and the isolated holebecomes uniformly, and it is resolved in ±0.1 μm defocus shown in rightside.

In the arrangement of the auxiliary pattern, if an insertion spaceexists between patterns, the auxiliary pattern may enclose twice thetarget pattern as shown in FIG. 26.

If Px is half pitch (Px/2=65, Py=√3Px/2) of the dense pattern in thehole with w=65 (nm) as shown in FIG. 25, although the size of the holeof the dense pattern is 65 (nm), the size of the isolated hole is set toWi=65*1.15=75 (nm) and the width of the auxiliary pattern is set toS=Wi*0.70=52 (nm) so that the size of the hole of the dense pattern isthe same as the size of the isolated hole. Thereby, the almost sameresult as FIG. 29 can be obtained. When the auxiliary pattern is doublyarranged around the target pattern, as compared with the case that theauxiliary pattern is singly arranged around the target pattern, thecorrection of the size of the isolated hole can be slight small and thewidth of the auxiliary pattern can be slight small. When the auxiliarypattern is doubly arranged around the target pattern, the exposureresult becomes somewhat good if the pattern is fine. However, even whenthe auxiliary pattern is singly arranged around the target pattern, theexpansion effect of resolution and depth of focus can be obtained if thewidth of the auxiliary pattern and the size of the isolated pattern arecorrected to the optimal.

Sixth Embodiment

Next, a description will be given of a manufacturing method of a checkerpattern by inserting the auxiliary pattern. A tessellated pattern asshown in FIG. 30A is Py=1.5 Px if a pitch in Y direction is Py and apitch in X direction is Px. In this case, since the pitch in Y directionis a forbidden pitch, the depth of focus cannot be obtained. The effectis achieved by inserting the auxiliary pattern to such pattern as shownin FIG. 30B. In FIG. 30B, white shows the target pattern and gray showsthe auxiliary pattern.

An auxiliary pattern is placed at the distance of Py=0.75Px in the ydirection, and at the distance of half-pitch (0.5px) in the x directionfrom a target pattern.

The mask uses the attenuated phase shift mask, and the size of thecontact hole is 60 nm, Px=120 nm, and Py=120*1.5=180 nm. The width ofthe auxiliary pattern is 60*0.67=40 (nm). The exposure result in thesame exposure condition is shown. (that is the ArF excimer laser and theimmersion exposure apparatus with a NA of 1.35) The illuminationcondition is the hexapole illumination and is a=0.86, 2α=2tan⁻¹(1/1.5)=67.4°. A size of a local light source is σr=0.10. Thepolarization is the radial polarization. FIGS. 32A and 32B shows atwo-dimension intensity distribution as the exposure result, and showsintensity with a intensity and a level contour line of ±20% to itsintensity. The half pitch in X direction of 60 nm is k₁=0.42 using k₁.

A pattern of an upper right of FIGS. 32A and 32B is an exposure resultof the pattern that includes the auxiliary pattern as shown in FIG. 30B,and a pattern of an lower left of FIGS. 32A and 32B is an exposureresult of the pattern that does not include the auxiliary pattern asshown in FIG. 30A. These patterns are exposed at the same time.Actually, the hole of the pattern of the lower left is bias-corrected sothat the size of the pattern after development becomes the same. FIG.32A shows the result in best focus, and FIG. 32B shows the result in±0.06 μm defocus. The contrast of the pattern that includes theauxiliary pattern (the pattern of the upper right) is better than thecontrast of the pattern that does not include the auxiliary pattern (thepattern of the lower left) in best focus and defocus.

The effect is achieved also to a hole that has different aspect ratio asshown in FIG. 33A. The aspect ratio of 2 is not special, but is merelyillustrative in addition to 1. In the size of the contact hole, thewidth in X direction is 130 nm, the width in Y direction is 65 nm and aninterval of X and Y directions is 65 nm, the pitch is Px=195 nm andPy=130 nm. If the auxiliary pattern is inserted, it becomes the patternas shown in FIG. 33B. The width of the auxiliary pattern in X directionis 130 nm*0.8=104 nm, and the width of the auxiliary pattern in Ydirection is 65 nm*0.8=52 nm. In the same exposure condition, the halfpitch in Y direction of 65 nm is k₁=0.45 using k₁. The illuminationcondition is the hexapole illumination as shown in FIG. 34 and isa=0.58, 2α=2 tan⁻¹(1/1.5)=73.7°. A size of a local light source isσr=0.10. The polarization is unpolarized light. The exposure result bythe ArF excimer laser and the immersion exposure apparatus with a NA of1.35 is shown. FIGS. 35A and 35B shows a two-dimension intensitydistribution as the exposure result, and shows intensity with apredetermined intensity and a level contour line of ±20% to itsintensity. FIG. 35A shows the result in best focus, and FIG. 35B showsthe result in ±0.10 μm defocus. The contrast is good in best focus anddefocus, and the depth of focus of about 0.2 μm is obtained. In thiscase, since the polarization is unpolarized light. An illumination ofthe attenuated phase shift mask with a radial polarization would improvethe contrast.

The effect is achieved also to a mask that includes dark lines in thebright field mask, such as Brick Wall pattern. The pattern shown in FIG.36A shows the target pattern as black and the transmitting part aswhite. If the auxiliary pattern is inserted to Brick Wall pattern, itbecomes the pattern as shown in FIG. 36B. The widths of the auxiliarypattern in X and Y directions is 65 nm×0.8=52 nm. In the same exposurecondition, the half pitch in Y direction is k₁=0.45 using k₁. Theillumination condition is the hexapole illumination as shown in FIG. 34and is a=0.58, 2α=2 tan⁻¹(1/1.5)=73.7°. A size of a local light sourceis σr=0.10. The polarization is unpolarized light. The exposure resultby the ArF excimer laser and the immersion exposure apparatus with a NAof 1.35 is shown. FIGS. 37A and 37B shows a two-dimension intensitydistribution as the exposure result, and shows intensity with apredetermined intensity and a level contour line of ±20% to itsintensity. FIG. 37A shows the result in best focus, and FIG. 37B showsthe result in ±0.10 μm defocus. The contrast is good in best focus anddefocus, the degradation in defocus is little, and the depth of focus of0.2 μm or more is obtained.

Here, a description will be given of a special case that the ratio of Pxand Py is Py=2Px. In this case, 2α=2 tan⁻¹(2/1*2)=90°, 2α=90° aresatisfied, two poles that do not exist on X axis among the hexapoleoverlap, and a quadrupole (cross pole) is formed. However, this isconsidered to be various hexapole. In other words, this is thequadrupole (cross pole) but generates the three beam interference.

Another example of Brick Wall pattern is shown. The pattern shown inFIG. 38 shows the target pattern as black and the transmitting part aswhite. The mask uses the attenuated phase shift mask, in the size of thecontact hole, if the width in X direction is 260 nm, the width in Ydirection is 65 nm and an interval of X and Y directions is 65 nm, thepitch is Px=325 nm and Py=130 nm. In the same exposure condition, thehalf pitch in Y direction of 65 nm is k₁=0.45 using k₁.

The illumination condition is the hexapole illumination as shown in FIG.39 and is a=0.57, 2α=2 tan⁻¹(2.5/2)=102.7°. A size of a local lightsource is σr=0.10. The polarization is unpolarized light. The exposureresult by the ArF excimer laser and the immersion exposure apparatuswith a NA of 1.35 is shown. FIGS. 40A and 40B shows a two-dimensionintensity distribution as the exposure result, and shows intensity witha predetermined intensity and a level contour line of ±20% to itsintensity. FIG. 40A shows the result in best focus, and FIG. 40B showsthe result in ±0.10 μm defocus. The contrast is good in best focus anddefocus, the degradation in defocus is little, and the depth of focus of0.2 μm or more is obtained.

Mr. H. Kim (SPIE 2003_(—)5040_(—)23) executes an optimization of theillumination condition in Brick Wall pattern. This is a method thatsearches the optimal condition by computer simulation. The articlediscloses an illumination with an effective light source shape shown inFIG. 41A. However, the detail illumination condition is not known. Thismethod cannot easily obtain the optimal solution of the illuminationcondition to the pattern with a certain pitch, and a general solution isnot disclosed. Although the illumination in the article closelyresembles the hexapole illumination, the distance from the pupil centerin each light source of the hexapole is not the same and the incidentangles of oblique incidence are not in agreement. The light source on Xaxis oblique incidence-illuminates the periodic pattern in X direction,and the light source that does not exist on X axis obliqueincidence-illuminates the periodic pattern in Y direction. Moreover,since the light source of oblique incidence to resolve in Y direction islarge, it becomes the illumination that emphasizes the resolution in Ydirection.

Here, a light source as shown in FIG. 41B is formed by lengthening thelight source portion that does not exist on X axis to outside based ona=0.57 and 2α=2 tan⁻¹(2.5/2)=102.7°, and Brick Wall pattern as shown inFIG. 38 is resolved. FIGS. 42A and 42B shows a two-dimension intensitydistribution as the exposure result. FIG. 42A shows the result in bestfocus, and FIG. 42B shows the result in 0.10 μm defocus. Since the lightsource portion to be not on X axis lengthens to outside and theresolution of the periodic pattern in Y direction is emphasized, theedge of the line pattern in Y direction is sharp and has good contrastin best focus and defocus. However, the end of the line pattern in Xdirection cannot easily resolve and cannot resolve in defocus.Therefore, if the interval of the line pattern in X direction is furtherlengthened, the illumination as shown in FIG. 41B cannot resolve.

Thus, in the hexapole illumination as shown in FIG. 39, the distancefrom the pupil center in each light source of the hexapole is the same,and the illumination condition is optimized so that the image is formedby the three beam interference. Thereby, the image with good balance inX direction and Y direction and good symmetry is formed. Moreover, thedegradation in defocus is little, and the practical depth of focus canbe obtained to the fine pattern.

Referring now to FIGS. 43 and 44, a description will be given of anembodiment of a device fabrication method using the above mentionedexposure apparatus 100. FIG. 43 is a flowchart for explaining how tofabricate devices (i.e., semiconductor chips such as IC and LSI, LCDs,CCDs, and the like). Here, a description will be given of thefabrication of a semiconductor chip as an example. Step 1 (circuitdesign) designs a semiconductor device circuit. Step 2 (maskfabrication) forms a mask having a designed circuit pattern. Step 3(wafer preparation) manufactures a wafer using materials such assilicon. Step 4 (wafer process), which is also referred to as apretreatment, forms the actual circuitry on the wafer throughlithography using the mask and wafer. Step 5 (assembly), which is alsoreferred to as a post-treatment, forms into a semiconductor chip thewafer formed in Step 4 and includes an assembly step (e.g., dicing,bonding), a packaging step (chip sealing), and the like. Step 6(inspection) performs various tests on the semiconductor device made inStep 5, such as a validity test and a durability test. Through thesesteps, a semiconductor device is finished and shipped (Step 7).

FIG. 44 is a detailed flowchart of the wafer process in Step 4. Step 11(oxidation) oxidizes the wafer's surface. Step 12 (CVD) forms aninsulating layer on the wafer's surface. Step 13 (electrode formation)forms electrodes on the wafer by vapor disposition and the like. Step 14(ion implantation) implants ions into the wafer. Step 15 (resistprocess) applies a photosensitive material onto the wafer. Step 16(exposure) uses the exposure apparatus 100 to expose a circuit patternof the mask onto the wafer. Step 17 (development) develops the exposedwafer. Step 18 (etching) etches parts other than a developed resistimage. Step 19 (resist stripping) removes unused resist after etching.These steps are repeated to form multi-layer circuit patterns on thewafer. The device fabrication method of this embodiment may manufacturehigher quality devices than the conventional one. Particularly, thefabrication method of this embodiment can stably resolve the finecontact hole, and provides the semiconductor device with high precision.Thus, the device fabrication method using the exposure apparatus 100,and resultant devices constitute one aspect of the present invention.

Thus, the image obtained by the three beam interference has goodcontrast and can obtain the large depth of focus to the fine pitch. Thetwo beam interference cannot easily realize the contrast of 40% or moreto finer half pitch. Although the four beam interference can obtain thecontrast, the half pitch that can obtain the depth of focus of 0.3 μm ormore is 0.5k₁ or more. Therefore, the three beam interference is thepractical and effective method to fine contact hole.

Furthermore, the present invention is not limited to these preferredembodiments and various variations and modifications may be made withoutdeparting from the scope of the present invention.

This application claims a foreign priority benefit based on JapanesePatent Application No. 2005-300662,filed on Oct. 14, 2005, which ishereby incorporated by reference herein in its entirety as if fully setforth herein.

1. An exposure method comprising: illuminating a mask that has a contacthole pattern using an illumination light; and projecting, via aprojection optical system, the contact hole pattern onto a substrate tobe exposed, wherein said contact hole pattern is a checker pattern thatincludes a plurality of periodic patterns, each of which has pluralcontact holes arranged in a first direction at a first pitch, and theplurality of periodic patterns are arranged in a second directionperpendicular to the first direction at a second pitch while shifting byhalf a pitch, wherein an effective light source formed on a pupil planein the projection optical system by the illumination light has sixpoles, wherein a distance between centers of the six poles and anoptical axis of the projection optical system is commonly a, whereinsaid centers of the six poles are located around the optical axis in adirection of an angle α to the first direction, wherein said angle α is0, 2α, π−2α, π, π+2α, and 2π−2α, wherein Pxo/2=(Px/2)NA/λ,Pyo/2=(Py/2)NA/λ, α=tan⁻¹ (Pxo/(2Pyo)), and a =1/(4(Pyo/2)/sin(2α)) aresatisfied, where Px is the first pitch, Py is the second pitch, NA is anumerical aperture of the projection optical system, and λ is awavelength of the illumination light, and wherein three beams amongdiffracted lights from the contact hole pattern interfere with eachother.
 2. An exposure method according to claim 1, wherein the contacthole pattern includes three or more contact holes that form a triangulargrid pattern.
 3. An exposure method according to claim 1, wherein saidcontact hole pattern includes a target pattern and an auxiliary patternhaving an area smaller than the target pattern, and wherein saidilluminating illuminates the mask using the illumination light so thatthe target pattern is resolved and the auxiliary pattern is preventedfrom being resolved.
 4. An exposure method according to claim 1, wherein1/(4(Pyo/2))/sin(2α)>1 and 1/(2(Pyo/2))/sin(tan⁻¹ (2sin(2α)))<1 aresatisfied.
 5. An exposure method according to claim 1, whereinPy=√3·Px/2=√3·P/2 and Px=P are satisfied.
 6. An exposure methodaccording to claim 4, wherein 0.33λ/(NA)<P/2<0.67λ/(NA) is satisfied. 7.An exposure method according to claim 4, wherein Po=(P/2)NA/λ,a=1/(3Po), and α=π/6 are satisfied.